Question: A cdf FX is stochastically greater than a cdf FY if Fx(t) FY(t) for all t and FX(t) < FY (t) for some t.

A cdf FX is stochastically greater than a cdf FY if Fx(t) ≤ FY(t) for all t and FX(t) < FY (t) for some t. Prove that if X ~ Fx and Y ~ FY, then
P(X > t) ≥ P(Y > t) for every t
and
P(X > t) > P(Y > t) for some t,
that is, X tends to be bigger than Y.

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